4b^2+40b=-84

Solution for 4b^2+40b=-84 equation:

Simplifying
4b2 + 40b = -84

Reorder the terms:
40b + 4b2 = -84

Solving
40b + 4b2 = -84

Solving for variable 'b'.

Reorder the terms:
84 + 40b + 4b2 = -84 + 84

Combine like terms: -84 + 84 = 0
84 + 40b + 4b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(21 + 10b + b2) = 0

Factor a trinomial.
4((7 + b)(3 + b)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(7 + b)' equal to zero and attempt to solve:

Simplifying
7 + b = 0

Solving
7 + b = 0

Move all terms containing b to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + b = 0 + -7
b = 0 + -7

Combine like terms: 0 + -7 = -7
b = -7

Simplifying
b = -7
Subproblem 2
Set the factor '(3 + b)' equal to zero and attempt to solve:

Simplifying
3 + b = 0

Solving
3 + b = 0

Move all terms containing b to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + b = 0 + -3
b = 0 + -3

Combine like terms: 0 + -3 = -3
b = -3

Simplifying
b = -3
Solution
b = {-7, -3}